Write an equation of the line that is:
a) parallel to the line y=2x-4, and has a y-intercept of 7
b) parallel to the line y-3x=6, and has a y-intercept of -2
c) parallel to the line 2x+3y=12, and that passes through the origin
d) perpendicular to the line y=3x+2, and has a y-intercept of 2
e) perpendicular to the line 3y+4x=18, and that passes through the origin
answer all these question

Lines that are parallel will have the same slope. Lines that are perpendicular will have slopes that are the negative reciprocal of each other.

(a) parallel to the line y=2x-4, and has a y-intercept of 7
slope of first line: 2
slope of second line: 2
y=mx + b
y=2x+7

(b) parallel to the line y-3x=6, and has a y-intercept of -2
y=3x+6
slope of first line: 3
slope of second line: 3
y=mx + b
y=3x-2

(c) parallel to the line 2x+3y=12, and that passes through the origin
3y=-2x+12
y=-2/3x+4
slope of first line: -2/3
slope of second line: -2/3
origin: (0,0)
y=mx + b
y=-2/3x + 0
y=-2/3x

(d) perpendicular to the line y=3x+2, and has a y-intercept of 2
slope of first line: 3
slope of second line: -1/3
y=mx + b
y=-1/3x + 2

(e) perpendicular to the line 3y+4x=18, and that passes through the origin
3y=4x+18
y=4/3x+6
slope of first line: 4/3
slope of second line: -3/4
origin: (0,0)
y=mx + b
y=-3/4x + 0
y=-3/4x